CN111327050B - Power distribution network reconstruction method and system containing distributed power supply based on binary differential evolution algorithm of hybrid strategy - Google Patents

Power distribution network reconstruction method and system containing distributed power supply based on binary differential evolution algorithm of hybrid strategy Download PDF

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CN111327050B
CN111327050B CN202010152439.1A CN202010152439A CN111327050B CN 111327050 B CN111327050 B CN 111327050B CN 202010152439 A CN202010152439 A CN 202010152439A CN 111327050 B CN111327050 B CN 111327050B
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邹锐
王超学
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Xian University of Architecture and Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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Abstract

The invention discloses a method and a system for reconstructing a power distribution network containing a distributed power supply based on a binary differential evolution algorithm of a hybrid strategy, wherein the method comprises the following steps: establishing a mathematical model of power distribution network reconstruction, and taking the minimum power distribution network loss of the power distribution network as a target function; determining the node type of the distributed power supply after the distributed power supply is merged into the power distribution network; encoding feasible solutions of the power distribution network by adopting an improved binary encoding mode, and initializing a population; selecting different mutation strategies by adopting a comparison mode of the current generation optimal individual and the previous generation optimal individual based on weight, and detecting and repairing invalid solutions appearing after mutation operation; adopting a heuristic self-adaptive cross probability calculation mode, adopting a harmony search strategy to optimize cross operation, and finally finishing the cross operation in a mode of taking a binary string as an individual; and updating the harmony search algorithm and the strategy of the harmony library to complete the selection operation. Compared with the prior art, the method has the advantages of high robustness, good optimizing performance, low convergence algebra and the like.

Description

Power distribution network reconstruction method and system containing distributed power supply based on binary differential evolution algorithm of hybrid strategy
Technical Field
The invention belongs to the technical field of power distribution network reconstruction, and particularly relates to a method and a system for reconstructing a power distribution network containing a distributed power supply based on a Binary Differential Evolution based Mixed Strategy (BDEMS) of a hybrid Strategy.
Background
The power distribution network is the last ring of connection between the power system and the users, and plays a vital role in ensuring normal power supply of the power system. The demands on the sustainability, the reproducibility of the power generation and the economy, the reliability of the power supply technology are also increasing. In the power Generation system, a Distributed Generation (DG) can supply electric power by using renewable energy such as wind energy and solar energy. Compared with the traditional hydraulic and thermal centralized power generation, the distributed power supply such as wind energy and solar energy has smaller capacity, but has the advantages of less environmental pollution, high economy, short arrangement period, more developed areas and the like. The DG is incorporated into a power distribution network for centralized power supply, and a distributed power supply and centralized power supply of clean energy are jointly used, so that the advantages and disadvantages of the DG can be mutually complemented, and the DG is a very potential power technology development direction.
However, when the DG is incorporated into the distribution network, the single power supply is changed into the multi-power supply, which directly causes the change of the power flow distribution of the distribution network, thereby reducing the voltage quality and increasing the network loss. The public data show that in 2016, the bus loss rate of the electric power in China is 5.32%, and the proportion of the electric power loss caused by unreasonable structure of the distribution network in the bus loss is as high as 55%, so that the power supply economy and practicability including DG are greatly reduced. Therefore, through researching the reconstruction of the power distribution network, the power supply quality can be effectively improved, the network loss of the network can be reduced, and the method has important research significance.
The power distribution network reconstruction problem belongs to one of optimization problems, a Differential Evolution (DE) is an excellent method mainly used for solving a continuous function combination optimization problem, and iteration steps of the DE include population initialization, variation operation, crossover operation and selection operation. However, the power distribution network reconstruction problem belongs to a discrete combination optimization problem, and the problem that solution vectors are difficult to correspond to a target function exists in the power distribution network reconstruction problem solved by directly applying the traditional DE algorithm. Further using a Binary code optimized DE algorithm, namely a Binary Differential Evolution (BDE), although the capability of the DE algorithm to solve the discrete problem can be improved, the traditional method for initializing the population by Binary codes also has the problem that a plurality of individuals correspond to the same solution vector, so that the algorithm generates a large amount of redundant search; the traditional mutation operation generates a large amount of invalid solutions to cause poor algorithm calculation performance, and the algorithm optimization performance caused by the imbalance of the global search capability and the local search capability of the mutation operation is low; the traditional binary coding mode may cause defects such as reduction of population diversity after cross operation.
In summary, it is an urgent need to improve the conventional BDE algorithm to improve the convergence speed, global optimization capability and ensure the convergence accuracy.
Disclosure of Invention
The invention aims to provide a power distribution network reconstruction method and system containing a distributed power supply based on a binary differential evolution algorithm of a hybrid strategy, so as to solve one or more technical problems. The method has good calculation performance and high probability of converging to the global optimal solution, and has good performance effect on the reconstruction problem of the complex power distribution network containing distributed power supplies and more nodes.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention discloses a power distribution network reconstruction method containing distributed power sources based on a binary differential evolution algorithm of a hybrid strategy, which comprises the following steps of:
step 1, collecting power distribution network data to be reconstructed, comprising the following steps: rated voltage, total number of nodes and branches, interconnection switch, impedance of each branch and bus terminal load; determining the type of a distributed power source incorporated into a power distribution network to be reconstructed; establishing a mathematical model of power distribution network reconstruction, and taking the minimum power distribution network loss of the power distribution network as a target function; determining the node type of the distributed power supply after the distributed power supply is merged into the power distribution network;
step 2, initializing a population, comprising: a binary coding mode based on a loop is adopted, only feasible solutions of the power distribution network are coded, the search space of the algorithm is reduced, and the convergence speed is improved;
and 3, performing mutation operation, comprising: based on the binary codes obtained in the step (2), performing mutation operation of the improved differential evolution algorithm by using a logic-based arithmetic expression to obtain binary mutation vectors; selecting different variation strategies by adopting a comparison mode of the current generation optimal individual and the previous generation optimal individual based on weight so as to improve the convergence speed of the algorithm; detecting invalid solutions which may appear after mutation operation, and providing an exclusive-or operation mode to repair the invalid solutions to finally obtain a mutation vector representing the valid solutions;
step 4, the operation of crossing and selecting includes: based on the binary variation vector obtained in the step 3, adopting a heuristic self-adaptive cross probability calculation mode to perform cross operation by individuals of the binary string; and (3) dynamically selecting the crossover probability CR according to the variation strategy performed in the step (3), providing a strategy improved crossover operation for fine adjustment of individuals based on a harmony search algorithm, so as to overcome the problem that population diversity is reduced possibly caused by invalid solution repair in the step (3), performing selection operation by comparing a test vector obtained by the crossover operation with a population worst vector, determining disconnected branch switches in each loop represented by the individuals in the population, and finally completing the optimized reconstruction of the power distribution network.
The invention is further improved in that in step 1, the minimum loss of the power distribution network is taken as an objective function, the reconstructed mathematical model of the power distribution network is expressed as,
Figure GDA0002454109180000031
in the formula, N is the total number of nodes in the power distribution network to be reconstructed, and P isi、Qi、Ri、UiRespectively representing active power, reactive power and resistance of the branch circuit i and a terminal node voltage value of the branch circuit i;
the voltage drop constraint of the distribution network to be reconstructed is expressed as,
Uimin≤Ui≤Uimax i＝1,...,N；
the line current value constraints of the distribution network to be reconstructed are expressed as,
Ii≤Iimax i＝1,...,N；
the power capacity constraints of the distribution network to be reconfigured are expressed as,
Si＜Simax i＝1,...,N；
in the formula of Ui、Uimin、UimaxRespectively representing the voltage amplitude of the node i and the upper limit and the lower limit thereof;
Iimaxis the maximum current of the branch;
Si、Simaxrespectively representing the power value flowing through each line and the maximum allowable value of branch capacity;
after the power distribution network to be reconstructed is reconstructed, the power distribution network is radial, and no loop or island exists.
In step 1, the determining the node type of the distributed power source after the distributed power source is incorporated into the power distribution network includes: the distributed power supply connected to the power distribution network is processed into two models: p, Q constant, the values of P and Q are known; p, V constant, the values of P and V are known; p, Q, V respectively represents active power, reactive power and voltage amplitude of the distributed power supply;
obtaining the current power distribution network loss P by calculating the power flow distribution of the power distribution network to be reconstructedLossAnd the lowest node voltage.
The further improvement of the present invention is that, initializing a population in step 2, and encoding a feasible solution of the distribution network by using a binary encoding method based on a loop includes:
step 2.1, determining a topological structure of the power distribution network to be reconstructed, closing all contact switches, and simultaneously determining a loop of the power distribution network based on the topological structure, wherein the loop is marked as n; wherein the loop is stored in a manner [ loop 1; loop 2; …, respectively; loop n ];
step 2.2, determining the number of effective branches in each loop in the n loops obtained in the step 2.1, and recording as k(s); wherein the effective branch is marked as aall(n)＝[a1,a2,…aj,…,ak]The topological network storage matrix A of the power distribution network to be reconstructed is represented as: a ═ aall(1),aall(2),…,aall(n)]TWherein A ∈ Rn×max[k(s)](ii) a For dimensions below max [ k(s)]By a 0-filling operation, the remaining loop dimension is max [ k(s)]The method meets the requirement of storage in a matrix mode, and is convenient for indexing when population individuals are generated subsequently and invalid solutions are checked;
step 2.3, storing each loop a in the matrix A according to the topological networkall(n) determining a set of binary code strings to represent a by decimal number with maximum index of effective branch and converting into binary numberall(n) disconnected node and marking the binary code as mnThe total length of the initial code is L ═ m1+m2+…+mnDetermining an initial search space of 2 for an improved differential evolution algorithmLBy eliminating invalid solutions, 2 can be further reducedLThe initial search space of (a);
step 2.4, set the population size NP, the population X is represented as,
Xi′(t)＝[x1,j(t),x2,j(t),…,xi′,j(t)]，
wherein x is an individual in the population, i' is 1,2, …, NP, t represents the t-th generation population, and j represents the dimension of the current individual; the population individuals x are converted into binary numbers in a random decimal number to generate the population individuals x.
A further development of the invention consists in that, in step 2.3, a for step 2.2allThe (n) 0-complement operation generates invalid binary code, and the improvement is that 0 to aallAnd (n) taking the maximum index value of the effective branch as an interval, randomly generating a decimal number, and converting the decimal number into a binary number as an individual in the population.
The further improvement of the invention is that the operation in step 3 is changed, and the method specifically comprises the following steps:
step 3.1, two different variant modes of operation are used, including: DE/rand/1/bin and DE/best/1/bin;
wherein, to satisfy binary code calculation, XOR is used
Figure GDA0002454109180000051
Means for "and" with
Figure GDA0002454109180000052
Means "or" is represented by "+";
the DE/rand/1/bin variation mode calculation expression is,
Figure GDA0002454109180000053
the DE/best/1/bin mutation pattern calculation expression is,
Figure GDA0002454109180000054
in the formula, F is a scaling factor and is generated by adopting random 0 or 1; p1, P2, and P3 are indices of an individual X in the population X, and satisfy that P1 ≠ P2 ≠ P3 ≠ i', and the index distance between two individuals is obtained as a hamming distance;
step 3.2, the best individual X of the current generationbest(t) and the best individuals X of the previous generationbest(t-1) comparing; wherein, if Xbest(t)-Xbest(t-1) > 0, performing global search by using DE/rand/1/bin in the t +1 generation; otherwise, using DE/best/1/bin to perform local search, and entering step 3.3;
step 3.3, recording the difference alpha between the current generation optimal individual and the previous generation optimal individual, wherein alpha (t) is Xbest(t)-Xbest(t-1); when in use
Figure GDA0002454109180000055
The algorithm converges to global optimum generation by generation, wherein delta t represents a plurality of generations between the current generation and a certain previous generation; when in use
Figure GDA0002454109180000056
At this time, whether to change the mutation mode in the next generation is determined by accumulating the weights.
In a further improvement of the present invention, in step 3.3, the determining whether to change the mutation pattern in the next generation by accumulating the weights includes:
setting a weight function f (x) which is monotonically increased in a definition domain (0, + ∞), nonlinearly mapping the recorded | alpha (t) | into f (x), wherein f (alpha (t)) is the weight represented by alpha (t), and performing normalization processing once in each generation, wherein the expression is as follows:
Figure GDA0002454109180000061
wherein f isw(x) Represents the normalized weight, fw(x)∈[0,1]；
When the algorithm converges to the global optimum, | alpha (t) | is subjected to nonlinear mapping and normalization to obtain a weight value, so that when | alpha (t) | is monotonically decreased, fw(x) Converge to 0, and the expression is
Figure GDA0002454109180000062
tmaxIs the maximum iteration number;
generating a random number u in the range of (0, 1); when in use
Figure GDA0002454109180000063
Representing the addition of several individual weights such that the weights sum
Figure GDA0002454109180000064
If the value is larger than the threshold value u, the algorithm is trapped in local optimization, and a DE/rand/1/bin variation mode is carried out in the next generation; if it is
Figure GDA0002454109180000065
The mutation pattern of DE/best/1/bin is still used in the next generation; where j' represents the current generation number that satisfies this step.
A further development of the invention consists in step 3.4 in that the number m of binary coded bits is based onnConfirming individuals which may generate invalid solutions after mutation operation, and detecting and repairing the individuals; wherein, the maximum effective index expressed by decimal number of the individuals which may generate invalid solution is converted into binary code k ', and the mutated individuals are compared with the corresponding individuals in k'. If the variation vector is smaller than the corresponding individual in k', no operation is performed and the step 4 is performed; if the individual of the variation vector is greater than or equal to the corresponding individual in k ', carrying out exclusive OR operation on the variation individual and the corresponding individual in k ' to generate a new variation vector V 'ij：
Figure GDA0002454109180000066
Simultaneously judge V'ijIf so, repeating the exclusive or operation with k' by using the newly generated invalid solution; if not, then V'ijRetained and used as a variation vector for subsequent steps.
The further improvement of the invention is that the crossing and selecting operation in the step 4 specifically comprises the following steps:
step 4.1, the two variant modes are represented in binary coding as,
DE/rand/1/bin＝0，DE/best/1/bin＝1；
when the return value is 0, the value of CR is as follows:
CR0＝0.2+β；
wherein β is subject to a normal distribution with a mean value of 0, and the variance is such that β fluctuates between [ -0.1,0.1 ];
at this time CR0∈[0.1,0.3]；
When the return value is 1, the value of CR is as follows:
Figure GDA0002454109180000071
in the formula, CRmin、CRmaxThe upper and lower limits of CR are 0.2 and 0.9 respectively, t is the current generation number, t is0Heuristic selection of 0.05tmax～0.1tmax，tmaxIs a preset maximum iteration number;
and 4.2, based on the variation vector, performing cross operation on individuals of the binary string, and improving the cross operation by adopting a strategy of fine adjustment on the individuals in the harmony search algorithm, so that the problem of reduction of population diversity possibly caused after invalid solution repair is performed in the step 3.2 is solved.
A further improvement of the invention is that in step 4.2, the interleaving operation is optimized using an improved harmonic fine tuning strategy, comprising:
when the cross trigger condition rand is not satisfiedi′jAnd (d) generating the individuals in the test vector by the individuals in the population, and determining whether to perform a fine-tuning strategy on the individuals to improve the cross operation by using Pitch Adjusting Probability (PAR) by using a harmony search algorithm. The method for fine tuning the individual by the harmony search algorithm according to the tone tuning probability PAR comprises the following steps:
generating a random number u 'in an interval (0,1), when u' < PAR:
xi′j＝xi′j±bw×u″，
where bw is the pitch adjustment bandwidth in the harmonic search algorithm and u' is another random number generated within the (0,1) interval. The pitch adjustment probability PAR is usually chosen in (0, 1).
Due to bw, u' and xi′jThe numerical value and the operation mode of the method are decimal, the direct modification to binary number and the operation can cause the failure of the fine adjustment result, so an improved fine adjustment method is used for operation:
generating a random number u 'in an interval (0,1), when u' < PAR:
xi′j＝Xbest,j，
and determining the pitch adjustment probability PAR in an adaptive manner:
Figure GDA0002454109180000081
wherein, according to the research conclusion of related published documents, the upper and lower limits of PAR are determined as PARmin＝0.25，PARmax0.55, t is the current evolution algebra, tmaxIs the maximum evolution algebra.
The expression of the crossover operation after optimization based on the harmony search strategy can be obtained as follows:
Figure GDA0002454109180000082
wherein m isi′j(t +1) is a variation vector Vi′j(t +1) individuals, Gi′And (t +1) is the generated test vector, and d is the dimension of the binary code m generated in the step 2.
Step 4.3, compare the test vector Gi′(t +1) and the value of the objective function represented by the worst solution vector for population X, if f (G)i′) Better than the worst solution vector in the population X, G isi′And replacing the worst solution vector to finish the selection operation, otherwise, not performing the selection operation. Simultaneously recording the current iteration times t, when t is more than or equal to tmaxStopping iteration and outputting the optimal solution in the population X; otherwise, recording t as t +1, and repeatingRepeating the steps 3 to 4.
The invention relates to a power distribution network reconstruction system containing a distributed power supply based on a binary differential evolution algorithm of a mixed strategy, which comprises the following steps:
the model building module is used for collecting the data of the power distribution network to be reconstructed and comprises the following steps: rated voltage, total number of nodes and branches, interconnection switch, impedance of each branch and bus terminal load; determining the type of a distributed power source incorporated into a power distribution network to be reconstructed; establishing a mathematical model of power distribution network reconstruction, and taking the minimum power distribution network loss of the power distribution network as a target function; determining the node type of the distributed power supply after the distributed power supply is merged into the power distribution network;
the coding module is used for coding feasible solutions of the power distribution network by adopting a coding mode of converting decimal numbers of the maximum effective branches into binary numbers in each loop, serving as population individuals in the improved differential evolution algorithm, and used for reducing the search space of the algorithm and improving the convergence speed;
the mutation operation module is used for performing mutation operation of the improved differential evolution algorithm by using a logic-based arithmetic expression based on the binary codes obtained by the coding module; selecting a variation strategy by adopting a comparison mode of the current generation optimal individual and the previous generation optimal individual based on weight so as to improve the convergence speed of the algorithm; determining individuals of certain variation vectors needing to be detected based on the binary coding length, and detecting and repairing invalid solutions in the individuals to ensure that solution vectors subjected to variation operation are strictly effective solutions;
the reconstruction module dynamically selects the cross probability CR according to a search mode carried out by the variation operation module by adopting a heuristic self-adaptive cross probability calculation mode based on the binary codes obtained by the coding module; performing bitwise cross operation by using a binary string, and performing a fine adjustment strategy on individuals based on a harmony search algorithm, so that the cross operation is improved, and the reduction of population diversity possibly caused after invalid solution repair is overcome; and reserving a better solution by comparing and replacing the test vector with the population worst solution vector, outputting an optimal solution vector when the current iteration number meets the maximum iteration number, determining the branch switch of each circuit to be disconnected according to the binary code of the solution vector, and finishing the optimal reconstruction of the power distribution network.
Compared with the prior art, the invention has the following beneficial effects:
in the method, the population initialization, mutation operation and selection operation parts of the traditional BDE algorithm are optimized. Aiming at the problem that the search space is too large due to the fact that a traditional BDE algorithm initializes a population based on a switch and a binary coding digit, a decimal number based on a loop and a maximum effective branch is converted into a binary number in a coding mode, so that invalid solutions are prevented from being generated, and the search space of the algorithm is reduced; meanwhile, a method based on weight accumulation is provided to select different variation modes, so that the capability of the algorithm to converge to a global optimal solution is improved; the detection and repair method for the invalid solution possibly occurring after the mutation operation is provided, so that the algorithm is ensured to search in less effective solution space, and the calculation time is reduced; a heuristic calculation method for performing cross operation on self-adaptive cross probability CR is provided, so that the optimization searching capability of an algorithm is improved; and an individual fine-tuning strategy based on a harmony search algorithm is provided to further improve cross operation and improve population diversity so as to increase the optimization performance of the algorithm.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art are briefly introduced below; it is obvious that the drawings in the following description are some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
Fig. 1 is a schematic flowchart of a method for reconstructing a power distribution network including distributed power sources based on a binary differential evolution algorithm of a hybrid strategy according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an IEEE33 node system in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a mutation operation selection method and invalid solution detection and repair process based on weight accumulation according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating a distribution of weight functions (tanh) used in a mutation operation selection method based on weight accumulation according to an embodiment of the present invention;
FIG. 5 is a cross-operation diagram of an example of an IEEE33 node system in an embodiment of the present invention;
fig. 6 is a schematic diagram of an IEEE69 node system according to an embodiment of the present invention.
Detailed Description
In order to make the purpose, technical effect and technical solution of the embodiments of the present invention clearer, the following clearly and completely describes the technical solution of the embodiments of the present invention with reference to the drawings in the embodiments of the present invention; it is to be understood that the described embodiments are only some of the embodiments of the present invention. Other embodiments, which can be derived by one of ordinary skill in the art from the disclosed embodiments without inventive faculty, are intended to be within the scope of the invention.
Referring to fig. 1, a method for reconstructing a power distribution network including a distributed power supply based on a Binary Differential Evolution based Mixed Strategy (BDEMS) of a hybrid Strategy according to an embodiment of the present invention includes the following steps:
and S1, determining a model of the distribution power source merged into the distribution network by taking the minimum network loss as a mathematical model of the reconstruction of the distribution network.
And S2, carrying out binary coding on the feasible solution of the power distribution network to be reconstructed based on a loop disconnection principle, and carrying out initialization of the population.
S3, performing mutation operation on the individuals in the step S2, providing a weight-based method to select different mutation modes, and detecting and repairing possible invalid solutions after the mutation operation.
And S4, providing a heuristic calculation mode of self-adaptive cross probability, performing cross operation in a mode of taking a binary string as an individual, further optimizing the cross operation by using a harmony search algorithm to perform a fine adjustment strategy on the individual, finally updating the population of the algorithm in a mode of replacing the worst harmony vector by the optimal harmony vector in the harmony search algorithm, completing selection operation, and stopping calculation and outputting an optimal solution if the current iteration number meets the requirement of the maximum iteration number.
In the embodiment of the present invention, the step S1 specifically includes the following steps:
step S11: when the minimum network loss is taken as a target function, the mathematical model of the power distribution network reconstruction is as follows:
Figure GDA0002454109180000111
wherein N is the total number of nodes in the power distribution network to be reconstructed, and P isi、Qi、Ri、UiAnd respectively representing the active power and the reactive power flowing through the branch i, the resistance of the branch i and the voltage value of the tail end node of the branch i.
And simultaneously, inequality constraint conditions comprise voltage drop constraint, line current value constraint and power supply capacity constraint:
Uimin≤Ui≤Uimax i＝1,...,N；
Ii≤Iimax i＝1,...,N；
Si＜Simax i＝1,...,N；
wherein, Ui、Uimin、UimaxThe voltage amplitude and the upper and lower limits of the node i are respectively; si、SimaxThe maximum allowable value of the power value flowing through each line and the branch capacity. Meanwhile, after the power distribution network to be reconstructed is reconstructed, the power distribution network is radial, and no loop or island exists.
Step S12: the incorporation of DGs causes the power distribution network load flow distribution to change, and further causes the network loss in the reconstructed mathematical model to change, so that DGs are uniformly processed into two models for different types of grid-connected DGs, and the network loss of the power distribution network is calculated by using a forward method on the load flow calculation method:
(1) model with constant P and Q. Such models are treated as "negative" loads, i.e., P ═ Pi、Q＝-Qi. P, Q respectively represents the active power and the reactive power of DG;
(2) model with both P and V constant, where P, V is the active power and voltage amplitude of DG, respectively. The model initial reactive power in this case is assumed to be Q ═ Q (Q)max+Qmin) And/2, further injecting reactive power into the network at each iteration as follows:
|ZPV|QPV＝UR_PV-|UPV|，
wherein, UPVThe node voltage obtained by the current calculation is obtained; u shapeR_PVA specified PV node voltage amplitude; zPVA corresponding self-impedance component for the PV node; qPVAnd in order to correct the reactive power which is injected into the network at the current node load.
In the embodiment of the present invention, the step S2 is based on a binary code initialization population mode of a loop, and takes an IEEE33 node system as an embodiment, and specifically includes the following steps:
step S21: IEEE33 node system according to a specific embodiment, as shown in fig. 2. The reference voltage of a 33-node system is 12.66KV, the total load is 3715kW + j2300kVar, 5 initially-disconnected interconnection switches are T33, T35, T34, T37 and T36 respectively, and the initial network loss is 202.7 kV. Further based on the 5 tie switches in the specific embodiment, the number of loops n is determined to be 5, and the number of active branches k in each loop is recorded to be [10,7,7,11,16 ═ at the same time]TAnd node a for each active branchall(n)＝[a1,a2,…aj,…,ak]Obtaining the dimension of a topological network storage matrix A of the IEEE33 node system as A ∈ R5×16While for dimensions below max [ k(s)]The loop of 16 carries out 0 complementing operation to satisfy the determination of the binary code bit number in the subsequent step and the elimination of invalid binary code, loop aall(n) may be expressed as:
aall(1)＝[2 3 4 5 6 7 33 20 19 18 0 0 0 0 0 0]；
aall(2)＝[21 35 11 10 9 8 33 0 0 0 0 0 0 0 0 0]；
aall(3)＝[9 10 11 12 13 14 34 0 0 0 0 0 0 0 0 0]；
aall(4)＝[3 4 5 25 26 27 28 22 23 24 37 0 0 0 0 0]；
aall(5)＝[6 7 8 34 15 16 17 36 32 31 30 29 28 27 26 25]；
wherein, aallThe non-zero element in (1) represents an active branch in the loop, and the zero element represents a non-active branch.
The topology network storage matrix a of the IEEE33 node system may be denoted as a ═ aall(1),aall(2),aall(3),aall(4),aall(5)]。
Step S22: the effective branch number k determined in step S21 is [10,7,7,11,16 ═ c]TAnd storing the matrix A, so that the binary code only represents the index value of the effective branch, can determine the loop a of the IEEE33 node systemall(n) each requires m1＝4、m2＝3、m3＝3、m4＝4、m5A binary string of 4. With aall(1)＝[2 3 4 5 6 7 33 20 19 18 0 0 0 0 0 0]For example, the effective branch k (1) ═ 10, and m needs to be used at minimum1A binary string of 4 is represented and when the randomly generated binary string is greater than 1001, an invalid solution of 0 for the open branch is indexed. To prevent a randomly generated invalid solution, the loop a is first closedall(n) all first branches' index values are represented in all-zero binary coding, and at the same time, in the interval [1, k-1 ] according to the determined number k of valid branches]Randomly generating a decimal number, and converting the decimal number into a binary number as an index value to represent the loop aall(n) open branch or tie switch.
Also with aall(1)＝[2 3 4 5 6 7 33 20 19 18 0 0 0 0 0 0]The binary coding of the active branches is specifically described for the example. The 1 st active branch is branch 2, and its topology network stores the matrix index value as a (1,1), which is represented by the binary string of the determined 0000. Simultaneously with aall(1) And the decimal index value of the middle effective branch is converted into binary number. Namely, the binary code with the minimum index of 1 is 0001, which indicates that the index value of the topology matrix is A (1, 2); the binary code with the maximum index value of 9 is 1001, which indicates that the index value of the topology matrix is a (1, 10). The binary coding mode can ensure that the individuals represented by the binary codes can be matched with the population in the initial generationThe switches with disconnected loops correspond to each other one by one, so that the influence of invalid solutions on the optimization performance of the algorithm is avoided.
Further based on the proposed coding scheme, when the tie switch for each loop of the IEEE33 node system is 33|35|34|37|36, the population based on binary coding can be represented as x 0101|001|101|1001| 0110. Meanwhile, based on the embodiment of the IEEE33 node system, the BDEMS algorithm can be obtained, wherein the length of the binary code required by each individual is
Figure GDA0002454109180000131
I.e. an initial search space of 218。
For those unfeasible solutions where there are not satisfying the constraints of step S1, the unfeasible solutions may be detected and repaired using any of the methods presently disclosed.
Step S23: setting the population size NP, the population X can be represented as Xi′(t)＝[x1,j(t),x2,j(t),…,xi′,j(t)]Wherein x is an individual in the population, i' is 1,2, …, NP, t represents the t-th generation population, j represents the dimension of the current individual, and in order to ensure that the population individual x meets the requirement of the step S21, the specific generation mode of the population individual is aall(1)＝[2 3 4 5 6 7 33 20 19 18 0 0 0 0 0 0]For example, it is first necessary to locate the interval [1, k-1 ]]Firstly, randomly generating a decimal number, converting the generated decimal number into a binary string, and then, obtaining 0001 binary code with the minimum random value of 1, which represents that the index value of the topological matrix is A (1, 2); the binary code with the maximum random value of 9 is 1001, which indicates that the index value of the topology matrix is a (1, 10). The binary coding mode can ensure that individuals represented by the binary codes can correspond to the switches disconnected by each loop one by one in the initial generation of the population, and the influence of invalid solutions on the optimization performance of the algorithm is avoided.
Meanwhile, the decimal index is converted into the binary coding mode, so that the binary coding of invalid nodes in 5 loops in the IEEE33 is reduced. Wherein a isall(1) The invalid node of is aall(1) 37.5% of the index length, and the rest 3 loop invalid nodes respectively account for 43.75% of the index length43.75%, 68.75% and 0%, the average is 38.75% less search space. According to the population individual generation mode of the binary code, the initial search space of the step S22 can be further reduced to 0.6125 × 218. BDE algorithm 2 relative to the traditional method37The search space and the encoding mode of binary encoding and individual many-to-one mapping are adopted, so that the BDEMS greatly reduces the search space and redundant search, and the optimizing capability is higher. Although the population initialized based on the encoding of the step does not have invalid solutions, the invalid solutions can still be generated after subsequent mutation operations. This problem will be further optimized in subsequent steps.
Referring to fig. 3, in the embodiment of the present invention, the method for selecting a mutation pattern based on weight and the method for detecting and repairing invalid solutions in step S3 specifically include the following steps:
step S31: the coding method in step S22 may cause the algorithm to converge to the local optimal solution, so according to the existing mutation operation mode, the DE/rand/1/bin with stronger global search capability and the DE/best/1/bin with stronger local search capability are selected as the search mode for BDEMS mutation operation. To ensure that the result is 0 or 1 for each element of the algorithm at the same time, a logical expression is used instead of an arithmetic expression, i.e. an exclusive OR
Figure GDA0002454109180000141
Means for "and" with
Figure GDA0002454109180000142
If "or" is indicated by "+", the DE/rand/1/bin variation mode calculation formula is:
Figure GDA0002454109180000151
the DE/best/1/bin variation mode calculation formula is as follows:
Figure GDA0002454109180000152
wherein F is a scaling factor, is generated by using random 0 or 1, P1, P2, and P3 are indexes of individuals X in the population X, and satisfy P1 ≠ P2 ≠ P3 ≠ i', and the index distance between two individuals is obtained as a hamming distance.
Step S32: when the current algebra is t, the current generation optimal individual is subtracted from the previous generation optimal individual, and if X is greater than t, the current generation optimal individual is subtracted from the previous generation optimal individualbest(t)-Xbest(t-1)＞0(Xbest(t) represents that the individual disconnected branch in the current population minimizes the network loss of the power distribution network), indicating that the algorithm may be trapped in local optimization, performing global search by using DE/rand/1/bin in the t +1 generation, otherwise performing local search by using DE/best/1/bin, and entering step S33.
Step S33: recording the difference alpha, alpha (t) X between the current generation optimal individual and the previous generation optimal individualbest(t)-Xbest(t-1). When the algorithm converges to global optimum, it should satisfy
Figure GDA0002454109180000153
Where Δ t denotes a number of generations between the current generation and a certain previous generation, and when the IEEE33 node system is used as an example, Δ t is 1. If it is
Figure GDA0002454109180000154
The representation algorithm may be involved in local optimization, but the criterion is determined by generating the individual in a random manner
Figure GDA0002454109180000155
It cannot be strictly stated that the algorithm is currently a local optimization. Thus when
Figure GDA0002454109180000156
If so, the method of accumulating weights provided in step 3.4 is carried out to further determine whether the mutation mode is changed in the next generation, otherwise, DE/best/1/bin is continuously used for local search;
step S34: selecting tanh function as weight function fw(x) As shown in fig. 4. The initial loss per unit (reference 202.7MV) of the embodiment IEEE33 is given in consideration of the domain range defined by the tanh function. Alpha (t) to be recorded) Non-linear mapping to fw(x) In, fw(| α (t) |) is the weight represented by α (t), and normalization processing is performed once in each generation:
Figure GDA0002454109180000157
at the same time, a random number u is generated in the range of (0,1) when
Figure GDA0002454109180000158
(j' represents the current generation number satisfying this step), and is based on fw(x) The convergence characteristic of (2) shows that the current generation optimal individual and a plurality of the previous generation optimal individuals are not monotonically decreased, and the weight sum of the individual is added to enable the weight sum
Figure GDA0002454109180000161
If the threshold value u is larger than the threshold value u, it can be determined that the algorithm is involved in local optimization, so that the DE/rand/1/bin mutation mode is performed in the next generation, and steps S31 to S34 are repeated. If it is
Figure GDA0002454109180000162
The mutation pattern of DE/best/1/bin is still used in the next generation and only steps S34 to S35 are repeated in said step S3.
Step S35: the effective branch number k determined based on step S22 is [10,7,7,11,16 ═ c]TAnd 5 loops of the IEEE33 node system require m, respectively1＝4、m2＝3、m3＝3、m4＝4、m5A binary string representation of 4. Wherein m is5The maximum index that can be expressed by 4 randomly generated binary codes is 16, which is an index of a valid solution, and the maximum index of the binary codes is not changed after the mutation operation of step S34 is performed. And m is1＝4、m2＝3、m3＝3、m4The maximum indices that can be expressed by 4-randomly generated binary codes are 7 and 16, i.e., the binary numbers of the variant individuals that can be obtained when step S34 is executed are larger than 1010, 111, 1011, resulting in invalid solutionsAnd (4) indexing. Therefore, it is necessary to detect and repair the individual j-1 to j-4 in the loop 1 to loop 4. The specific detection and repair method comprises the following steps:
converting the indexes 10 and 11 of the most significant solutions of the loop 1 and the loop 4 into binary codes k' 1010|1011, and transforming the mutation vectors V generated by the mutation pattern of step S34i′From 1 to 4, compared with k'. If the variation vector is smaller than the corresponding individual in k', no operation is performed and step S4 is executed; if the individual of the variation vector is greater than or equal to the corresponding individual in k ', carrying out exclusive OR operation on the variation individual and the corresponding individual in k ' to generate a new variation vector V 'ij：
Figure GDA0002454109180000163
Judging V'ijIf j 1 to j 4 are still invalid solutions, repeating the exclusive-or operation by using the new invalid solutions; if not, then V'ijRetained and used as a variation vector for subsequent steps.
Similarly, taking the example IEEE33 as an example, when the number j of loop 1 is 1 and 1100 is obtained after the mutation operation of step S34, the number j is greater than the number 1 of individuals 1010 in k', that is, an invalid solution is generated, and after the exclusive or operation is performed, the invalid solution is restored to the invalid solution
Figure GDA0002454109180000164
If the repaired invalid solution is smaller than the 1 st individual 1010 in k', step S4 may be further performed.
Through the invalid solution detected and repaired in the step, the search space of the algorithm can be strictly controlled to be 0.6125 multiplied by 2 in the step S2218In the search space, but the new solution repaired based on the xor operation reduces the population diversity to some extent, which leads to the algorithm being easy to converge to the locally optimal solution, and therefore, the proposed algorithm needs to be further optimized in the subsequent steps.
In this embodiment of the present invention, the step S4 is a heuristic calculation method of adaptive crossover probability and crossover operation and selection operation improved by harmonic search strategy, and specifically includes:
step S41: the two variation modes of the step 3) are represented by binary coding as follows: according to the public conclusion that the existing larger CR is favorable for global search and the smaller CR is favorable for local search, when the step S3 is completed and the return value is judged to be 0, the smaller CR is selected. Dynamic and small CR is beneficial to promoting global search, and when the return value is 0, the value of CR is as follows:
CR0＝0.2+β；
wherein β is subject to a normal distribution with a mean value of 0, and the variance is such that β fluctuates approximately at [ -0.1,0.1 [)]In this case, CR can be obtained0∈[0.1,0.3]。
When the return value is 1, the value of CR is as follows:
Figure GDA0002454109180000171
wherein, CRmin、CRmaxThe upper and lower limits of CR are 0.2 and 0.9 respectively, t is the current generation number, t is0Can select 0.05t in a heuristic mannermax～0.1tmax，tmaxIs a preset maximum number of iterations. Testing of various embodiments, including the IEEE33 node, has shown that tmax100 is a reasonable choice.
Thus, the calculation of CR may be calculated by a piecewise function:
Figure GDA0002454109180000172
step S42: based on the binary coding individuals generated in the steps S2 and S3, on the basis of using the cross formula of the BDE as the cross formula of the BDEMS, considering the problem of reduced population diversity caused by the proposed binary coding method and the repair method of the invalid solution in the mutation operation, the cross operation in the conventional BDE algorithm is optimized in a manner of fine tuning a single sum sound (i.e., individuals of the population in the BDEMS) when the pitch adjustment probability PAR is satisfied in the harmony search algorithm, so as to increase the population diversity and reduce the probability of convergence of the algorithm on the local optimal solution.
The formula for the cross-operation of the conventional BDE algorithm is:
Figure GDA0002454109180000181
wherein m'ij(t +1) is a variation vector Vi′j(t +1) individuals, Gi′(t +1) is the generated test vector, randi′jIs a random number in (0,1), d is the dimension of the binary code m generated in step S2, m is 18, and the rest symbols have the same meaning as above. As a specific example, the IEEE33 node system may determine that d is 5.
According to the cross formula of BDE algorithm, when the triggering condition rand is satisfiedi′jWhen CR or j ═ rand (d) is not more than CR, the vector of variation m'ij(t +1) as a test vector Gi′(t +1) of an individual; when the triggering condition rand is not satisfiedi′jCR or j ═ rand (d), the number of individuals in the population xi′j(t) as test vector Gi′(t +1) and performing crossover operation.
The way in which new harmony is generated in the harmony search algorithm is very similar to the mutation, crossover operations in the BDE algorithm. Wherein the new harmony and harmony memory bank in the harmony search algorithm can be analogized to the test vector G in the BDE algorithmi′(t +1), population. But differs in that when vector G is testedi′(t +1) (or new harmony) when the individuals in the population (or harmony memory bank) are selected (as shown by the BDE algorithm not satisfying the triggering condition rand)i′jCR ≦ or j ═ rand (d)), the harmony search algorithm will fine tune the individuals in the population (and the individuals in the vocal memory bank) further based on the pitch adjustment probability PAR. The fine tuning mode is as follows:
firstly, generating a random number u 'in a (0,1) interval, when u' < PAR:
xi′j(t)＝xi′j(t)±bw×u″
where bw is the pitch adjustment bandwidth in the harmonic search algorithm and u' is another random number generated within the (0,1) interval. The pitch adjustment probability PAR is usually chosen in (0, 1).
The method for finely adjusting the individuals (namely the individuals in the BDE population) in the harmony memory bank in the harmony search algorithm can solve the problem that the algorithm is easy to converge to a local optimal solution due to the fact that population diversity is reduced after invalid solutions are repaired in the step S35.
Considering that the individuals in the population are discrete values represented in binary code, the fine tuning cannot be directly achieved by directly using the pitch adjustment bandwidths bw and u ″, and therefore, an improved harmonic fine tuning strategy is used based further on the harmonic fine tuning strategy of the harmonic search algorithm:
when PAR < u', let [ min ]]f(Xbest,j(t)) in established populations, individual Xbest,j(t) substitution of xi′j(t); when PAR ≧ u', fine adjustment is not performed.
Based on the harmony search strategy, the crossover formula of the traditional BDE is improved as follows:
Figure GDA0002454109180000191
similar to the cross probability CR, when the PAR value is small, the probability of disturbance of the contemporary population individual is high, which is beneficial to global optimization; when the PAR value is larger, the disturbance probability of the contemporary population is low, which is beneficial to local optimization. Therefore, one PAR value approach is used:
Figure GDA0002454109180000192
wherein, PARmin＝0.25，PARmax0.55, t is the current evolution algebra, tmaxIs the maximum evolution algebra.
A schematic diagram of the cross-operation, particularly improved with the harmonic search strategy, is shown in fig. 5.
Step S43: calculating the test vector G generated in the step S42i′The corresponding optimized objective function value, if f (G)i′) Better than the worst solution vector in the population X, G isi′And replacing the worst solution vector to finish the selection operation, otherwise, not performing the selection operation. Simultaneously recording the current iteration times t, when t is more than or equal to tmaxStopping iteration and outputting the optimal solution in the population X; otherwise, t is recorded as t +1, and step S3 to step S4 are repeated.
Referring to fig. 6, in another embodiment of the present invention, an IEEE69 node system is used to illustrate the optimal reconfiguration result of the present invention, and the IEEE69 node system is shown in fig. 6. The rated voltage of a 69-node system is 12.66KV, the total load is 3802.2kW + j2694.6kVar, 5 initially-disconnected interconnection switches are T70, T71, T73, T69 and T72, and the initial grid loss is 224.97 kV. IEEE33 and IEEE69 node systems are taken as specific embodiments, grid-connected nodes, modes and capacities of DGs are shown in table 1, after DGs are connected to the grid, the connection switches initially disconnected in the IEEE33 and IEEE69 node systems in the embodiments are kept unchanged, initial grid loss is respectively changed into 115.11KW and 146.32KW, and per unit values of initial lowest node voltages are respectively 0.9266p.u and 0.9286 p.u. DG specific data are derived from the open literature.
TABLE 1 DG installation node and Capacity
Figure GDA0002454109180000201
For two different embodiments, the population size NP is set to 60, the maximum number of iterations is set to 100, and the upper and lower limits of the pitch regulation bandwidth are respectively the PARmin＝0.25，PARmaxThe upper and lower limits of the crossover probability CR are CR, respectivelymin＝0.2、CRmax0.9. The voltage reference was 12.66 kV.
After the DGs are connected to the grid, the BDEMS respectively tests results of the two standard examples, the network switching state, the network loss and the lowest node voltage of the power distribution network, as shown in Table 2, wherein the Table 2 is an optimization result after the DGs are connected to the grid.
TABLE 2 optimization results after DG grid connection
Figure GDA0002454109180000202
According to the optimization results of the two specific embodiments after the DG is connected to the grid as shown in table 2, the open fulcrum switches of the two embodiments and the corresponding optimization results are consistent with the optimal solutions obtained by the related publications, so that the network loss of the two embodiments can be reduced by 33% and 40%, respectively, and the lowest node voltage is increased from 0.9266p.u to 0.9630p.u, and from 0.9286p.u to 0.9468p.u, respectively. The BDEMS algorithm can effectively achieve the optimization purpose of reducing the network loss and the voltage deviation.
The advantages of the proposed method in terms of computational performance are further illustrated by comparing two embodiments after DG integration by using a traditional BDE algorithm and the BDEMS algorithm proposed by the present invention. The performance of the BDE algorithm was compared to that of the BDEMS, as shown in table 3, table 3 compares the performance of the BDE algorithm to that of the BDEMS algorithm.
TABLE 3 BDE Algorithm vs BDEMS Algorithm Performance comparison
Figure GDA0002454109180000211
The results of 50 independent tests of the conventional BDE algorithm and the proposed BDEMS algorithm are shown in table 3. For the embodiment IEEE33, the average convergence algebra of BDEMS is 11.7, the minimum convergence algebra is only 6, and the results of 50 independent tests converge to the optimal solution, which is superior to the conventional BDE algorithm in both convergence algebra and probability of convergence to the optimal solution. For the embodiment IEEE69, the conventional BDE algorithm has only 7 convergence to the optimal solution, and the average convergence algebra is as high as 95.5, but the proposed BDEMS algorithm can also converge to the optimal solution in 50 independent tests, and the average convergence algebra is 18.6 and the minimum convergence algebra is 13, which is far better than the conventional BDE algorithm. Meanwhile, compared with the nodes in the embodiment IEEE33, the optimization results of the more complex embodiment IEEE69 have the same number of times of convergence to the optimal solution, and the average convergence algebra difference is not large, which can further explain that the BDEMS also has good optimization performance on the optimization reconstruction problem of the complex distribution network including DG.
In summary, the present invention relates to a method for reconstructing a power distribution network including distributed power sources based on a binary differential evolution algorithm of a hybrid strategy, which specifically includes the following steps: 1) establishing a mathematical model of power distribution network reconstruction, and considering the node type of the DG merged into the power distribution network; 2) an improved loop-based binary coding mode is provided for coding feasible solutions of the power distribution network to complete population initialization; 3) carrying out mutation operation of the proposed method by using an arithmetic expression based on logic, further providing a comparison mode of a current generation optimal individual and a previous generation optimal individual based on weight to select a proper mutation strategy, detecting invalid solutions which may appear after mutation operation, and repairing the invalid solutions by using XOR operation; 4) and a heuristic self-adaptive cross probability calculation mode and cross operation improved by a harmony search strategy are provided, the selection operation is completed by comparing and replacing a test vector obtained by the cross operation with a population worst solution vector, and finally the solution of the power distribution network to be reconstructed is obtained. Compared with the prior art, the method has the advantages of strong optimization capability, good robustness and excellent performance in solving the reconstruction problem of the complex power distribution network containing the DGs.
Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can make modifications and equivalents to the embodiments of the present invention without departing from the spirit and scope of the present invention, which is set forth in the claims of the present application.

Claims (8)

1. A power distribution network reconstruction method containing distributed power sources based on a binary differential evolution algorithm of a hybrid strategy is characterized by comprising the following steps:
step 1, collecting power distribution network data to be reconstructed, comprising the following steps: rated voltage, total number of nodes and branches, interconnection switch, impedance of each branch and bus terminal load; determining the type of a distributed power source incorporated into a power distribution network to be reconstructed; establishing a mathematical model of power distribution network reconstruction, and taking the minimum power distribution network loss of the power distribution network as a target function; determining the node type of the distributed power supply after the distributed power supply is merged into the power distribution network;
step 2, initializing a population, comprising: a binary coding mode based on a loop is adopted to code feasible solutions of the power distribution network to complete population initialization, so that the search space of an algorithm is reduced, and the convergence speed is increased;
and 3, performing mutation operation, comprising: based on the binary codes obtained in the step (2), carrying out mutation operation of a differential evolution algorithm by using a logic-based arithmetic expression to obtain binary mutation vectors; the mutation operation adopts a comparison mode of the current generation optimal individual and the previous generation optimal individual based on the weight to select a mutation strategy so as to improve the convergence speed of the algorithm; detecting and repairing invalid solutions which appear after mutation operation, so that mutation vectors obtained after mutation operation are valid solutions;
step 4, the operation of crossing and selecting includes: based on the binary variation vector obtained in the step 3, a heuristic self-adaptive cross probability calculation mode is adopted, and cross operation is carried out in a mode that a binary string is taken as an individual; dynamically selecting a cross probability CR according to the search mode performed in the step 3; adopting a harmony search algorithm to improve the cross operation of the individual fine adjustment strategy; updating a harmony search algorithm and finishing selection operation by using a harmony library strategy, and finally determining the branch switches disconnected with each loop to finish the optimized reconstruction of the power distribution network;
in step 2, the encoding of the feasible solution of the power distribution network by using the loop-based binary coding method includes:
step 2.1, determining a topological structure of the power distribution network to be reconstructed, determining a loop of the power distribution network based on the topological structure, and recording the loop as n; wherein the loop is stored in a manner [ loop 1; loop 2; …, respectively; loop n ];
step 2.2, determining the number of effective branches in each loop in the n loops obtained in the step 2.1, and recording as k(s); wherein the effective branch is marked as aall(n)＝[a1,a2,…aj,…,ak]Of the distribution network to be reconfiguredThe topology network storage matrix a is represented as: a ═ aall(1),aall(2),…,aall(n)]TWherein A ∈ Rn×max[k(s)](ii) a For dimensions below max [ k(s)]By a 0-filling operation, the remaining loop dimension is max [ k(s)]Ensuring that the requirements of generating population individuals are met in the subsequent steps;
step 2.3, storing each loop a in the matrix A according to the topological networkall(n) dimension, determining a set of binary code strings to represent aall(n) disconnected node and marking the binary code as mnThe total length of the code L is L ═ m1+m2+…+mnDetermining the search space of the initial algorithm to be 2L；
Step 2.4, set the population size NP, the population X is represented as,
Xi′(t)＝[x1,j(t),x2,j(t),…,xi′,j(t)]，
wherein x is an individual in the population, i' is 1,2, …, NP, t represents the t-th generation population, j represents the dimension of the current individual, and the population individual x is generated by a binary number converted by a random decimal number.
2. The method for reconstructing the power distribution network with the distributed power sources based on the binary differential evolution algorithm of the hybrid strategy as claimed in claim 1, wherein in step 1, the minimum network loss of the power distribution network is taken as an objective function, and the mathematical model of the reconstruction of the power distribution network is expressed as,
Figure FDA0003529982850000021
in the formula, NP is the total number of nodes in the power distribution network to be reconstructed, Pi、Qi、Ri、UiRespectively representing active power, reactive power and resistance of the branch circuit i and a terminal node voltage value of the branch circuit i;
the voltage drop constraint of the distribution network to be reconstructed is expressed as,
Uimin≤Ui≤Uimax i＝1,...,N；
the line current value constraints of the distribution network to be reconstructed are expressed as,
Ii≤Iimax i＝1,...,N；
the power capacity constraints of the distribution network to be reconfigured are expressed as,
Si＜Simax i＝1，...，N；
in the formula of Ui、Uimin、UimaxRespectively representing the voltage amplitude of the node i and the upper limit and the lower limit thereof;
Iimaxis the maximum current of the branch;
Si、Simaxrespectively representing the power value flowing through each line and the maximum allowable value of branch capacity;
after the power distribution network to be reconstructed is reconstructed, the power distribution network is radial, and no loop or island exists.
3. The method for reconstructing a power distribution network including distributed power supplies based on a binary differential evolution algorithm of a hybrid strategy according to claim 1, wherein in step 1, the determining the node type of the distributed power supplies incorporated into the power distribution network comprises: the distributed power supply connected to the power distribution network is processed into two models: p, Q constant, the values of P and Q are known; p, V constant, the values of P and V are known; p, Q, V respectively represents active power, reactive power and voltage amplitude of the distributed power supply;
obtaining the current power distribution network loss P by calculating the power flow distribution of the power distribution network to be reconstructedLossAnd the lowest node voltage.
4. The method for reconstructing a power distribution network including distributed power sources based on a binary differential evolution algorithm of a hybrid strategy as claimed in claim 1, wherein in step 2.3, the values from 0 to a are usedall(n) the maximum index value of the valid branch is the interval, randomly generating a decimal number, and converting the decimal number into a binary number as an individual in the population to prevent a of step 2.2all(n) inThe 0 complement operation produces invalid binary code while reducing by 2LThe search space of (2).
5. The method for reconstructing the power distribution network including the distributed power sources based on the binary differential evolution algorithm of the hybrid strategy as claimed in claim 1, wherein the step 3 specifically comprises the following steps:
step 3.1, two different variant modes of operation are used, including: DE/rand/1/bin and DE/best/1/bin;
wherein the exclusive OR is used
Figure FDA0003529982850000031
Means for "and" with
Figure FDA0003529982850000032
Means "or" is represented by "+";
the DE/rand/1/bin variation mode calculation expression is,
Figure FDA0003529982850000033
the DE/best/1/bin mutation pattern calculation expression is,
Figure FDA0003529982850000034
in the formula, F is a scaling factor and is generated by adopting random 0 or 1; p1, P2, and P3 are indices of an individual X in the population X, and satisfy that P1 ≠ P2 ≠ P3 ≠ i', and the index distance between two individuals is obtained as a hamming distance; i ═ 1,2, …, NP;
step 3.2, the best individual X of the current generationbest(t) and the best individuals X of the previous generationbest(t-1) comparing; wherein, if Xbest(t)-Xbest(t-1) > 0, performing global search by using DE/rand/1/bin in the t +1 generation; otherwise, using DE/best/1/bin to perform local search, and entering step 3.3;
step 3.3, recording the difference alpha between the current generation optimal individual and the previous generation optimal individual, wherein alpha (t) is Xbest(t)-Xbest(t-1); when in use
Figure FDA0003529982850000041
The algorithm converges to global optimum generation by generation, wherein delta t represents a plurality of generations between the current generation and a certain previous generation; when in use
Figure FDA0003529982850000042
At this time, whether to change the mutation mode in the next generation is determined by accumulating the weights.
6. The method for reconstructing a power distribution network including distributed power sources based on a binary differential evolution algorithm of a hybrid strategy according to claim 5, wherein in step 3.3, the determining whether to change the variation pattern in the next generation by accumulating the weights comprises:
setting a weight function f (x) which is monotonically increased in a definition domain (0, + ∞), nonlinearly mapping the recorded | alpha (t) | into f (x), wherein f (alpha (t)) is the weight represented by alpha (t), and performing normalization processing once in each generation, wherein the expression is as follows:
Figure FDA0003529982850000043
wherein f isw(x) Represents the normalized weight, fw(x)∈[0,1]；
When the algorithm converges to the global optimum, | alpha (t) | is subjected to nonlinear mapping and normalization to obtain a weight value, so that when | alpha (t) | is monotonically decreased, fw(x) Converge to 0, and the expression is
Figure FDA0003529982850000044
Generating a random number u in the range of (0, 1); when in use
Figure FDA0003529982850000045
Representing the addition of several individual weights such that the weights sum
Figure FDA0003529982850000046
If the value is larger than the threshold value u, the algorithm is trapped in local optimization, and a DE/rand/1/bin variation mode is carried out in the next generation; if it is
Figure FDA0003529982850000047
The mutation pattern of DE/best/1/bin is still used in the next generation; where j' represents the current generation number that satisfies this step.
7. The method for reconstructing the power distribution network including the distributed power supplies based on the binary differential evolution algorithm of the hybrid strategy as claimed in claim 5, further comprising:
step 3.4, based on binary coded number mnConfirming individuals which may generate invalid solutions after mutation operation, and detecting and repairing the individuals;
wherein, the maximum effective index expressed by decimal number of the individuals which can possibly generate invalid solution is converted into binary code k ', and the mutated individuals are compared with the corresponding individuals in k'; if the variation vector is smaller than the corresponding individual in k', adjusting to step 4; if the individual of the variation vector is greater than or equal to the corresponding individual in k ', carrying out exclusive OR operation on the variation individual and the corresponding individual in k ' to generate a new variation vector V 'ijThe expression is as follows,
Figure FDA0003529982850000051
judging V'ijIf so, repeating the exclusive or operation with k' by using the new invalid solution; if not, then V'ijReserving and using the vector as a variation vector of a subsequent step; vi′jAnd performing exclusive-or operation on the variation vector individuals vi' j.
8. The method for reconstructing the power distribution network including the distributed power sources based on the binary differential evolution algorithm of the hybrid strategy as claimed in claim 5, wherein the step 4 specifically comprises the following steps:
step 4.1, the two variant modes are represented in binary coding as,
DE/rand/1/bin＝0，DE/best/1/bin＝1；
when the return value is 0, the value of CR is as follows:
CR0＝0.2+β；
wherein β is subject to a normal distribution with a mean value of 0, and the variance is such that β fluctuates between [ -0.1,0.1 ];
at this time CR0∈[0.1,0.3]；
When the return value is 1, the value of CR is as follows:
Figure FDA0003529982850000052
in the formula, CRmin、CRmaxThe upper and lower limits of CR are 0.2 and 0.9 respectively, t is the current generation number, t is0Heuristic selection of 0.05tmax～0.1tmax，tmaxIs a preset maximum iteration number;
step 4.2, based on the variation vector, performing cross operation by using individuals of the binary string; improving cross operation by adopting a strategy of fine adjustment of individuals in the harmony search algorithm to prevent reduction of population diversity possibly caused after invalid solution repair is carried out in the step 3.2;
wherein, when the cross trigger condition rand is not satisfiedi′jCR or j ═ rand (d), generating the individuals in the test vector by the individuals in the population, and determining whether to perform a fine-tuning strategy on the individuals to improve the cross operation by using the harmony search algorithm and the pitch adjustment probability; the method for fine tuning an individual by a harmony search algorithm with a pitch adjustment probability PAR comprises the following steps:
generating a random number u 'in an interval (0,1), when u' < PAR:
xi′j＝xi′j±bw×u″，
wherein bw is a pitch adjustment bandwidth in the harmony search algorithm, and u' is another random number generated within the (0,1) interval;
the pitch adjustment probability PAR is usually chosen in (0, 1);
to prevent the generation of the magnetic field due to bw, u' and xi′jThe numerical value and the operation mode are decimal, the binary number is directly modified, the fine adjustment result is possibly invalid due to operation, and the fine adjustment method is adopted for operation and comprises the following steps:
generating a random number u 'in an interval (0,1), when u' < PAR:
xi′j＝Xbest，j，
the tone adjustment probability PAR is determined in a self-adaptive mode, and the expression is as follows:
Figure FDA0003529982850000061
wherein the upper and lower limits of PAR are defined as PARmin＝0.25，PARmax0.55, t is the current evolution algebra, tmaxIs the maximum evolution algebra;
the expression of the crossover operation after the harmony search strategy optimization is as follows:
Figure FDA0003529982850000071
wherein m isi′j(t +1) is a variation vector Vi′j(t +1) individuals, Gi′(t +1) is the generated test vector, d is the dimension of the binary code m generated in the step 2;
step 4.3, compare the test vector Gi′(t +1) and an objective function value represented by the worst solution vector of the population X; wherein if f (G)i′) Better than the worst solution vector in the population X, G isi′Replacing the worst solution vector, otherwise, not performing any operation; note the bookRecording the current iteration times t, wherein when t is more than or equal to tmaxStopping iteration and outputting the optimal solution in the population X; otherwise, recording t as t +1, and repeating the step 3 and the step 4;
wherein, randi′jA cross-triggering condition for the ith' j individual of the population, j represents the dimension of the current individual, xi′jIs the i' j individual of the population, Xbest，jAnd the population is the optimal individual under the current iteration times.
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